Alarm Calls as Costly Signals of Anti-Predator Vigilance: The Watchful Babbler Game

Alarm-calling behavior is common in many species that suffer from predation. While kin selection or reciprocal altruism are typically invoked to explain such a behaviour, several authors have conjectured that some alarm calls may instead be costly signals sent by prey to inform approaching predators that they have been detected. We develop a general game-theoretic model -- the Watchful Babbler game -- in which prey signal awareness to predators. We derive necessary and sufficient conditions for alarm calls to function as honest signals. We show that signals can honestly reveal prey awareness if (1) the prey's sense of predation risk accurately reflects the probability that the predator is present, and (2) greater awareness of the predator allows the prey a great chance of escape. When honest signalling is possible, the model predicts that prey will be more willing to signal when predators are common that when predators are rare, and that greater pursuit costs to the predator will allow cheaper signals by the prey.